N EXPERIMENTAL TEST ON DYNAMIC CONSUMPTION AND LUMP SUM …

AN EXPERIMENTAL TEST ON DYNAMIC CONSUMPTION AND LUMP‐SUM

PENSIONS1

Authors

ENRIQUE FATÁS JUAN A. LACOMBA FRANCISCO LAGOS ANA I. MORO‐EGIDO LINEEX

Campus Tarongers Universidad de Valencia

46022 Valencia Spain

Departament of EconomicsFaculty of Economics University of Granada Campus La Cartuja s/n

18071 Granada Spain

Phone +34963828643 Fax +34963828415 [email protected]

Phone +34958249605Fax +34958249995 [email protected] [email protected] [email protected]

ABSTRACT

This article examines the potential risks on consumption behavior of lump‐sum payments in public pension systems. Lump‐sum payments can be consumed too fast and generate an increase of poverty rates. We experimentally investigate retirement consumption behavior in an inter‐temporal decision‐making setting. Subjects make consumption and saving decisions in an environment with two central features: first, there exists a decreasing probability of survival; and second, in addition to the regular income they get while active, they receive a unique lump‐sum payment when retired. The results of this paper indicate that in the vast majority of periods subjects over‐save. Moving the lump‐sum payment into earlier periods makes the effect eventually deeper: subjects adopt larger precautionary saving decisions. JEL category: C91, H55, J26. Keywords: Experimental test, consumption, savings, lump‐sum payment.

1 We thank people from CREED (Amsterdam) for helpful comments during the elaboration of the experimental design and seminar participants at Malaga, Tucson, Granada and Rome. Financial support from the Spanish Ministry of Education and Science, the Regional Government of Andalucia and Fundación Centro de Estudios Andaluces is gratefully acknowledged.

I. INTRODUCTION

The reform of Social Security systems is now one of the main issues on the

economic policy agenda of most industrialized countries. It is widely considered that,

unless serious changes take place, the aging of the population implying a rise in the

number of retirees relative to that of workers will threaten the viability of Pay‐As‐You‐Go

public pension systems in the long‐run.

Besides, this threat is being reinforced by the progressive reduction in the

retirement age of the working population. Pension systems in virtually all OECD countries

in the mid‐1990s made it financially unattractive to work after the age of 55.1 Indeed, the

general consensus in the theoretical literature related to Social Security and retirement

decisions is that pension systems create enormous incentives to leave the labour force

early. 2 This large decline in labour force participation is attributed to the specific fact that

to keep on working implies a reduction in the present value of total pension benefits. That

is, it is considered that the drop in pension wealth acts as an implicit tax on income from

continued work and as such is a clear incentive to retire early.

Reforms aiming to increase the effective retirement age to improve the financial

problems of public pensions systems have mainly focused on the reduction of this implicit

tax on prolonging the working period.

It is considered that when the increase in pension benefits is exactly offset by the

higher cost in terms of contributions and foregone pensions, the pension system is not

distorting the retirement decision. That is, the pension systems that are marginally

actuarially fair do not distort the individual retirement decisions. For this reason, the main

economic policy measures move in the direction of strengthening the link between life‐

time contributions and pension benefits.3

However, Cremer, Lozachmeur and Pestieau (2006) argue that “while there is no

doubt that retirement systems induce an excessive bias towards early in many countries, a

complete elimination of this bias (i.e., a switch to an actuarially fair system) is not the right

answer. This is so and for two reasons. First, some distortions are second‐best optimal.

Second, depending on the political process, it may either not be feasible or alternatively it

may tend to undermine the political support for the pension system itself.” 4

Therefore, a key question is whether or not there exist alternative reforms to

increase the effective retirement age. Orszag (2001), related to U.S. Social Security,

considered that transforming Social Security's delayed retirement credit (given to people

working between the ages of 62 and 65 in the U.S.) into a lump‐sum payment rather than

an increased monthly payment would likely encourage people to defer retirement.

This question is addressed in Fatas, Lacomba and Lagos (2007). They find that the

more concentrated the payments (shifting from annuity into lump‐sum), the more

postponed the retirement decisions. This results suggests, in the line of Orszag (2001), that

reforms aimed to delay effective retirement ages should transform the increases in

pensions due to the additional years of work (after the standard retirement age) into a

lump‐sum payment rather than an increased periodic payment. Additionally,

Fetherstonhaugh and Ross (1999), using a questionnaire, find evidence that people would

be more willing to delay retirement if they received a lump‐sump payment rather than an

increased annuity.

Furthermore, it is likely that this transformation including a lump‐sum payment

would be easier to implement. In the U.S. private industry, whose retirement benefits may

be distributed in several alternative ways, using some type of lump‐sum benefit as a

payment option has become popular as an alternative to annuity payments (see Moore

and Muller, 2002, Blostin, 2003 or Butrica and Mermin, 2006).

However, the incorporation of a lump‐sum payment as a measure to delay

retirement decisions requires further analysis before receiving full consideration by

policymakers. As Orszag (2001) also states, paying lump‐sum payments might result in

increases in poverty rates among those who already delay their retirement decisions after

the normal retirement age if the lump sums were mostly consumed rather than saved.

Little is known about how quickly retirees would spend down their lump‐sum

payments, or how these reforms would affect consumption patterns. Butrica and Mermin

(2006), using data from the Health and Retirement Study (HRS), examine how household

expenditures among adults aged 65 and older vary by the degree of annuitization. They

find that if Social Security was completely privatized, and retirees did not annuitize,

discretionary spending could increase by as much as 22 percent for married adults and 38

percent for unmarried adults. However, other studies have shown that consumption

usually declines at retirement. This decline has increasingly been referred to as the

retirement consumption puzzle. See Fisher et al (2005) for references.

These opposite results suggest that more research is needed before unambiguous

conclusions can be made. This is precisely the aim of this work: to provide additional

empirical evidence to this debate. To this end, we consider an experimental investigation

to test the potential effects on consumption behavior of implementing a lump‐sum

payment in a public pension system. We also analyze how closely the predictions of the

optimality theory fit the actual behavior of subjects in a lab.

To our knowledge, this is the first experimental approach to examine a dynamic

saving‐consumption problem in a retirement framework. The experimental design is based

on two central features: first, there exists a decreasing probability of surviving which

implies an uncertain future income; and, secondly, there are two sequences of income,

one when individual works and another when she is retired.

The results of this paper indicate that subjects over‐react to the lump‐sum

payments, as they briefly consume above their optimal dynamic consumption paths.

However, and on aggregate, the general picture goes in the opposite direction. In the vast

majority of periods they over‐save rather than over‐consume. This result holds for both the

periods prior to the lump‐sum payment and no income periods, when smoothing becomes

more difficult. Moving the lump‐sum payment into earlier periods (so, increasing the

number of periods with no income at all) seems to have a counterintuitive effect. Subjects

tend to over‐react even more and adopt precautionary saving measures. Our results

suggest that Social Security reforms aimed at moving from traditional annuitized pensions

to lump‐sum payments might not yield increases in poverty rates.

This paper is organized as follows. Section 2 briefly surveys the experimental

literature on this topic. Section 3 develops the theoretical model, while section 4 presents

the experimental design and procedures. Section 6 presents our results and the last one

concludes.

II. EXPERIMENTAL BACKGROUND

In the experimental literature into consumption behaviour under uncertainty there

exist few contributions but relevant ones. For instance, Hey and Dardadoni (1988) describe

a large‐scale experimental investigation to test the implications of expected utility

maximization on optimal consumption behaviour. They find that the actual behaviour in

the lab differs significantly from the optimal behaviour, and that the comparative static

implications of actual behaviour agree with those of optimality theory. Carbone and Hey

(2004) investigate the over‐sensitivity of consumption to current income. They adopt a

simple model in which income in any period can take just one of two values: employment

and unemployment. Unlike neoclassical theoretical predictions about smooth consumption

over time, they find that subjects over‐react. That is, their results show a close relationship

between consumption and current income.

On the other hand, Ballinger et al (2003) study social learning about the life cycle

saving task. They use experimental methods to study a household inter‐temporal choice

problem. Subjects participate in three‐member “families”. Second and third “generation”

subjects observe and/or communicate with their “antecedent” first or second generation

subject. They find that later generations perform significantly better than earlier

generations. Brown, Camerer and Chua (2006) establish potential ways in which

consumers can attain near‐optimal consumption behaviour. In line with Ballinger et al

(2003), individual and social learning mechanisms are proposed to be one possible link.

They find that while consumers persistently spend too much in early periods, they learn

rapidly from their own experience and from experience of others to consume amounts

close to optimal levels.

Our work presents some interesting differences with regard to all above mentioned

papers. In order to capture a retirement and pension system benchmark, we focus on how

subjects make saving and consumption choices with two novel features. First, subjects face

a decreasing probability of surviving across periods. Second, participants receive three

different levels of income according to a retirement period (R hereafter): i) a constant level

of income during each period before R (as worker); ii) a higher lump‐sum of income in R

(the first period as retired); and iii) nothing from R on.

III. THE MODEL

Before we proceed with the experimental design and results, in this section we are

going to characterize the optimal consumption decisions using a standard model. Consider

an individual who has to decide on his optimum consumption at different age in presence

of uncertainty about the length of life. Suppose that this is the only uncertainty that the

individual faces. Let T>0 be the planning horizon, that is, maximum lifetime. Lifetime

uncertainty is presented by a survival distribution function, F(t) non increasing in age, 0 ≤ t

≤ T, that satisfies F(0)=1.5 All individuals are assumed to have the same survival distribution

function.

Denote consumption at age t by c(t), where c(t)≥0. Utility from consumption at

different ages is separable and independent of age. There is no subjective discount rate.6

We use a specific utility function, u(c) that displays risk‐aversion, and to ensure an interior

solution, satisfies the Inada conditions.7 When working, the individual provides one unit of

labor. Contingent on survival, the individual works between ages 0 and R, 0<R<T, that is,

there exists a mandatory retirement age that occurs at R. The individual's objective

function is to maximize the non discounted expected utility V

)).(u( F(t)T

1t

tcV ∑=

= (1)

Let wages at age t, be w(t)≥0. Savings earn a zero rate of interest.8 With no initial

assets, the individual's assets at age t, S(t), are equal to the cumulative savings. Feasible

consumption plans must have non‐negative assets at all ages

∑∑==

=t

1j

R)min(t,

1j)( -w(j))( jctS . (2)

We assume that w(t)=w for all 0<t<R, therefore the restriction becomes

[ ] ∑=

−=t

1j

)( -,)1(min)( jctwwRtS . (3)

The choice of the optimum consumption path will depend on the insurance options

available. Relative to this benchmark case, we analyze an alternative scenario, in which

individuals will receive a unique lump‐sum payment at the beginning of the retirement

period. The total value of expected contributions has to be equal than the lump‐sum

payments, that is,

LS )( w F(t)1-R

1t

RF=∑=

τ , (4)

then the lump‐sum payment is

)( w)(

F(t) w

1-R

1t RHRF

LS ττ ==∑= . (5)

Restriction on savings is now

[ ] ],1[)( -)1(,min)(t

1j

RtjcwtLStS ∈∀−= ∑=

τ . (6)

This theoretical model will be used to measure to which extent subjects deviate

form the optimal consumption path in the experiment.

IV. EXPERIMENTAL DESIGN AND PROCEDURES

Our experimental design tries to capture some actual features of an actuarially fair

public pension system with a unique lump‐sum payment.9 The experiment consists of

three sequences of at most 30 rounds and one decision per round. See Table 1 into

Appendix.

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Insert Table 1 here ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Each round is characterized by a probability of surviving. As the round number

increases, the probability of surviving decreases. In each round reached, subject either

survives or not. A subject reaches a round if, and only if, she has survived all earlier rounds.

During the first R‐1 rounds, similar to wage earnings, subject receives 85

experimental units in each reached round (Income).

In round R, subjects receive the present value of the total pension benefits as a

unique lump‐sum payment. As a strategy to analyze the effect of the length of the

retirement period on savings and spending decisions, we design two treatments. In

Treatment 1 (hereafter LS10) the round R is the 10th and in Treatment 2 (hereafter LS15)

the round R is the 15th.

We consider a gross wage of 100 experimental units and a tax rate of 15%. Thus, in

order to reflect an actuarially fair pension system, the lump‐sum payment in LS10 is equal

to 191.25 experimental units (with R=10) and in LS15 is equal to 345 experimental units

(with R=15) following equation (5).

In the remaining rounds subjects receive no income at all. Therefore, in LS10 and in

LS15 subjects have at most 19 and 14 rounds with no income, respectively.

In each round subjects have to make a unique decision about how to divide the

Available Cash into consumption and savings. The available cash comes from the addition

of the income received in that period and what is not consumed in previous rounds (their

cumulative savings). So, income can be saved to provide wealth but savings earn no

interest and borrowing is not allowed, that is, subjects cannot spend more than their

Available Cash.

Let C denote the amount of experimental units converted into points by subjects in

each round (their consumption). Subjects are informed of the conversion scale (from

experimental units to points, converted into real euros at the end of the experiment): C

experimental units generate 20*Square Root (C) points. A table mapping how different

consumption choices are converted into points (euros) is given separately to subjects.

As mentioned above, subjects play three sequences. They are told that at the end

of the experiment they will be privately paid in cash the total amount of points converted

from experimental units of one of the three sequences (randomly chosen). They are also

told that any unconverted experimental unit remaining at the end of any sequence is

worthless.

A total of 39 undergraduate students in Business and Economics from the

University of Valencia took part in the experiment. All sessions were run at the Laboratory

for Research in Experimental Economics (LINEEX) and standard electronic recruitment

procedures were used to collect the subject pool. All subjects participating in the

experiment had previously participated (weeks before the experiment was run) in other

sessions facing a Raven test, a risk aversion test and a basic socioeconomic survey.10 The

list of participants in every session was randomized to control for any reputation or group

identity effect. Anonymity was preserved using random codes and these tests were paid

independently.

At the beginning of the experiment, subjects entered the laboratory and were

randomly seated in a private cubicle. Experimental instructions were read aloud by the

experimenter (instructions are provided in the Appendix). To make sure subjects

understood the logic of the game, subjects completed a quiz before the experiment began.

Explanations were repeated until all subjects passed the quiz (nobody made a mistake

almost from the beginning, quiz available from authors upon request).

At the end of the experiment subjects were privately paid with an exchange rate of

125 experimental units = €1 for one of the three sequences, chosen at random. On average

an experimental session lasted less than 90 minutes, the average earnings were around

€27 and the maximum earnings peaked above €40.

The experiment consisted of two treatments: LS10 and LS15. 20 subjects

participated at LS10 and 19 subjects at LS15.

V. RESULTS

Table 2 presents the summary statistics of the individuals’ decisions about

consumption, their cumulative savings and available cash at the beginning of each period,

for both the LS10 and LS15 treatments, by sequences. The number of survived periods in

the last row denotes the average number of rounds that subjects were alive and making

decisions. Average life is almost identical in both treatments (21.96 versus 21.31, as

expected in a pure randomly driven process).

By pure inspection, average consumption is higher in LS15 than in LS10. This follows

the experimental design, as subjects get a higher lump‐sum and get a positive income

during a higher number of periods in LS15. However, the more interesting information

regarding treatment effects comes from the next two variables. Both the average

cumulative savings and the available cash are a direct consequence of subjects’ decisions

in both treatments. Again, by pure inspection, subjects save considerably more in LS10

(152.8) than in LS15 (101.4): the difference is around 50%. This suggests that subjects in

the worst scenario are able to save more to protect themselves from the higher number of

periods with no income. Moreover, the average available cash is larger in LS10, in spite of

the fact that available cash is the sum of cumulative savings and income (by definition,

larger in LS15 than in LS10). Over‐saving behaviour in LS10 more than compensates this

difference.

No clear differences are observed across sequences within each treatment in

consumption and savings. The actual consumption and saving choices do not show a clear

(increasing or decreasing) trend as participants play more sequences. However, the

standard deviation falls as subjects make more decisions. Besides, this reduction in the

standard deviation across sequences seems to be systematic for all available variables.

That is, in a very preliminary way, subjects seem to adjust better as the number of

decisions increases.

The descriptive information shown above is not enough to answer our main

research question. In order to learn about subjects’ capabilities to get close to the optimal

consumption path, we need to measure the distance between actual decisions and our

theoretical benchmark.

We include two measures of divergence between actual and optimal behaviour. In

our view, there are two plausible ways of thinking about optimality in this context. The first

way is to define optimal consumption as the level of consumption calculated in the first

period for the rest of the life‐time profile. We will call this optimal consumption the ex‐

ante optimal consumption (EAOC). To compute EAOC we solve the dynamic optimization

problem in period zero to find the optimal smoothed consumption path. The policy

consequences of this approach to optimal decisions are straightforward: EAOC would be

the rational choices done by a benevolent social planner.

The second approach to optimality takes as the natural analysis unit the per‐round

individual decision. For every subject and every available cash amount, based on her

previous decisions, we compute the optimal consumption for every period, contingent on

the fact that (i) she is alive and (ii) owns a given actual positive wealth. This alternative

approach is a kind of natural basis for assessing the optimality of subjects’ decisions

dynamically. We call this ex‐post optimal consumption (EPOC).

Note that EAOC and EPOC have different meanings. The natural interpretation for

EAOC comes from the policy side: it is a general average measure of the adjustment of the

population (in our case, the subject pool) to the optimal path in welfare terms. Significant

deviations in this ex ante measure can be associated to welfare losses. EPOC gives

additional valuable information about the optimality of decisions at the individual level.

For every subject, in every period, it defines the optimal decision, contingent on the fact

that she is still making decisions over her individual level of wealth.

To facilitate the comparison of actual and optimal consumption levels over all

individuals we plot them. Figure 1 and 2 (3 and 4) correspond to average consumption and

cumulative savings in LS10 (LS15). In Figures 1 and 3, the actual consumption paths are

compared with EAOC and EPOC, while the associated optimal cumulative savings are used

in Figures 3 and 4.

In all cases both a risk aversion rate of .50 and a risk aversion rate of .28 are used to

check whether our results are robust to changes in risk aversion rates. The reasons for this

duality are twofold: on the one hand, a constant risk aversion rate of .50 is implicitly used

in the payoff function converting points into earnings.11 In addition, it was the mode

obtained in our risk aversion test. On the other hand, a risk aversion coefficient of .28 is

the average constant risk aversion rate of our subjects, measured by our risk aversion test.

[Figures 1 and 3 around here]

Unlike previous experimental papers, we find no evidence of over consumption in

the first rounds. On the contrary, our participants under‐consume in this earliest periods.12

This under‐consumption behaviour lasts until round 5 in LS10 and round 10 in LS15 using

the EAOC as a benchmark, while it holds in almost all rounds when the EPAC measure is

used. The results are qualitatively identical for both risk aversion measures.

From an ex ante perspective, and before the lump‐sum period comes, consumption

exhibits some inertia and subjects fail to smooth it. Relative to the EAOC path, subjects

over consume temporarily around the lump‐sum period, in rounds 8 to 11 in LS10 and

rounds 11 to 15 in LS15. However, this over consumption disappears when EPOC is used as

the reference point. With the exclusion of the very same period when the lump sum is

received, and only under a high risk aversion rate, subjects under consume in all periods

relative to the optimal path.

Interestingly, after the lump‐sum payment period, when subjects get no income at

all, participants in the experiment performed relatively well adjusting their behaviour to

the optimal path. Rather to consume their available income immediately after the lump‐

sum period, they keep on smoothing their consumption and adjust it to the optimal path in

a more than reasonable way.

A natural way to back up these descriptive comments is to have a look at the

evolution of cumulative savings over time in Figures 2 and 4. Subjects perform saving

choices in a relatively poor manner, in the sense that they over‐save in all periods in LS10,

regardless of the risk aversion rate used in the analysis. In LS15 subjects also over‐save in a

vast majority of periods, with the notable exception of periods around the lump‐sum

payment, when their reaction to the sharp increase in income is not compensated by a

parallel jump in savings. This general behavioural pattern does not change after receiving

the lump‐sum payment. It suggests that savings tend to be precautionary, with the

exception of the periods in which the high lump‐sum is received.

[Figures 2 and 4 around here]

Before we proceed with a more formal analysis of the experimental data it is worth

to note that our design can be considered as a kind of a strong test for over‐saving (and

under‐consumption). On the one hand, in Hey and Dardadoni (1988) and Carbone and Hey

(2004) the rate of return per period is known and certain, for all money saved. On the

other, in Ballinger et al (2003) and Brown, Camerer and Chua (2006) the incentives to save

money are embedded in their particular utility function, so saving is salient for subjects.

In our experimental design savings yields no returns. Our utility function, though

concave, differs of the ones used by Ballinger et al (2003) and Brown, Camerer and Chua

(2006) to avoid the salience of saving money. Additionally, subjects were not punished in

any specific way when their consumption was critically low, as no negative utility was

associated to a zero consumption level. We additionally paid very much attention to keep

framing as neutral as possible to avoid any kind of demand effect.

In a more formal way, we run some regressions to explore the determinants of

decisions. The dependent variable is the log of absolute deviation from optimality (both

relative to EAOC and EPOC: LD‐EAOC and LD‐EPOC). A negative coefficient means that the

corresponding independent variable lowers the deviation from optimality. Since the

dependent variable is the logged deviation, the coefficient means that a variable causes a

certain percentage of increase or decrease in deviation relative to when this variable is

absent.

We consider different groups of explanatory variables. Dumbreak is a dummy that

takes the value of 1 for all LS10 data, 0 otherwise, and it intends to capture the existence

of any treatment effect. Seq2 (Seq 3) takes the value of 1 when data is generated in the

second (third) sequence of 30 rounds.

As the probability of survival decreases with the number of periods played, we

include both a Period and a Period Squared variable. Hand in hand with the increasing

uncertainty (measured by the decreasing probability of survival), we expect participants to

make worse decisions as the number of periods increases, so we expect a positive

coefficient for this variable. The Period Squared variable simply takes into account any

possible non‐linearity that the period variable may have.

Risk is the risk aversion of subjects, as measured by the Holt and Laury risk aversion

test. The original value range (from 0 to 10), is decomposed into three values: 0 if subject is

risk loving, 1 if she is risk neutral and 2 if she is risk averse. Raven Test is the ratio of correct

answers in the test (a non verbal IQ test) run by all subjects participating in the

experiment. Sex is a dummy variable to control for gender effects (0 for females, 1 for

males).13 We report the estimation results in Table 3.

[Table 3 around here]

The first result emerging from Table 3 is that timing matters when dealing with

lump sum schemes. Postponing the retirement period and getting the lump sum later,

significantly increases the deviation from the optimal path. Even when subjects get a

positive income fewer times in LS10, they are relatively better able to cope with the

optimization problem and smooth their consumption over time.

No sequence dummy is significant, so our results suggest that there is very little

learning across stages, if any. Coefficients on Period and Period Squared show that, as

expected, deviations increase as more periods are played, but at a decreasing rate. Risk

aversion is significant. Risk‐averse subjects outperform risk lovers (as the negative

coefficients show). Surprisingly enough, a better performance in the non‐verbal

intelligence test (the “Raven test”) is related to an increase in the distance to optimal

consumption levels. We do not have a solid explanation for this finding. Finally, males

appear to deviate more in almost all cases.

Following Brown, Camerer and Chua (2006), we want to check whether a natural

behavioural explanation for the observed patterns of consumption is the existence of a

“rule of thumb”. Subjects simply spend a fixed fraction of their current income or a fraction

of available cash. To investigate this alternative explanation, we ran regressions in which

the log of actual consumption is regressed against the optimal level of consumption and

either current income or available cash (i.e, income plus cumulative savings). Table 4

summarizes these results.14

[Table 4 around here]

Table 4 suggests that subjects mainly focus on their current income when dealing

with consumption decisions. Besides, the coefficient of Income is larger than that of

Available cash, which means that subjects decide their consumption levels regardless of

their savings. This is consistent with the over‐saving behavioural pattern. The increment in

the R‐squared value is small when considering Available cash but large in the case of

Income.

VI. CONCLUSIONS

One of the proposals to delay the effective retirement age is to transform the

increases in pensions due to the additional years of work into a lump‐sum payment rather

than an increased periodic payment. This idea was first suggested by Orszag (2001) for the

U.S. Social Security. He considered that transforming Social Security's delayed retirement

credit (given to people working between the ages of 62 and 65 in the U.S.) into a lump‐sum

payment would likely encourage people to defer retirement.

However, this measure risks increasing poverty rates. People who do not annuitize

much of their retirement wealth might spend too quickly the lump‐sum payment reducing

income at very old ages. In this paper we have tested in the laboratory the potential

effects on consumption behavior of implementing a lump‐sum payment. Our main

conclusion is that this might not be the case. The introduction of a unique lump‐sum

payment generates a behavioral overreaction in the opposite direction: rather than

consuming too much, too fast, our subjects show a persistent precautionary saving

behavior.

The policy consequences of our experiment are that transforming (at least,

partially) pension benefits into lump‐sum payments might not increase elderly poverty

rates.

An additional risk, pointed by Orzsag (2001), comes from the political pressure to

extend lump‐sum payments to those who are younger than the regular retirement age.

Such an extension would raise the risk of increasing elderly poverty rates. The analyses of

results in our LS10 treatment, relative to the LS15, suggest the opposite: the earlier and

the lower the lump‐sum payment, the stronger the saving reaction.

This paper is the first step on the experimental analysis of consumption behavior

during retirement. Although we believe that our findings might help to achieve proper

Social Security reforms, we are also aware of its limitations. For instance, as Orszag (2001)

states, one important issue is whether the lump‐sum payment should be an option

available in addition to the existing scheme, or should simply replace it. If the system is

voluntary, selection effects across alternatives could raise costs to the Social Security

system (i.e., those with shorter life expectancies could disproportionately choose the

lump‐sum payment, while those with longer life expectancies could disproportionately

choose the annuity option). A choice between the two systems should be incorporated in

future experimental treatments of the problem. This is the topic of our ongoing research.

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VIII. APPENDIX

TABLE 1:EXPERIMENTAL DESIGN

Rounds Pobability of surviving

LS10 Income

LS15 Income

Available Cash

Consumption Savings Obtained Points

1 1 85 85 85 ‐‐‐ ‐‐‐ ‐‐‐

2 29/30 85 85

3 28/29 85 85

4 27/28 85 85

5 26/27 85 85

6 25/26 85 85

7 24/25 85 85

8 23/24 85 85

9 22/23 85 85

10 21/22 85 85

11 20/21 191,25 85

12 19/20 85

13 18/19 85

14 17/18 85

15 16/17 85

16 15/16 345

17 14/15

18 13/14

19 12/13

20 11/12

21 10/11

22 9/10

23 8/9

24 7/8

25 6/7

26 5/6

27 4/5

28 3/4

29 2/3

30 1/2

ºº 0,00

TABLE 2: DESCRIPTIVE STATISTICS LS10 LS15

Averages Total Seq = 1 Seq = 2 Seq = 3 Total Seq = 1 Seq = 2 Seq = 3Consumption 43,82 49,32 40,27 43,74 66,22 65,89 68,11 65,11 [44,20] [50,51] [44,61] [36,62] [44,65] [50,35] [44,18] [40,47] Cum. Savings 152,8 148,0 149,6 161,4 101,4 111,8 89,4 102,5 [187,35] [198,69] [187,81] [176,36] [135,31] [144,99] [128,05] [132,75] Available cash 196,6 197,3 189,9 205,2 167,6 177,7 157,5 167,6 [191,28] [197,28] [196,21] [179,00] [135,89] [144,09] [127,74] [135,25] # Survived periods 21,96 19,76 24,37 20,64 21,31 20,91 19,13 23,18 [7,12] [8,04] [5,95] [6,75] [7,08] [7,96] [7,50] [5,43]

# Obs. 1002 275 418 309 945 281 278 386

Std errors in brackets

TABLE 3: REGRESSION ANALYSIS

SIGMA=0.50 SIGMA=0.28 LD‐EAOC LD‐EPOC LD‐EAOC LD‐EPOCDumbreak ‐0.553*** ‐0.079 ‐0.538*** ‐0.139* [0.117] [0.071] [0.129] [0.067] Seq 1 0.057 0.050 0.150 0.048 [0.193] [0.117] [0.212] [0.109] Seq 2 ‐0.162 0.066 ‐0.075 ‐0.032 [0.181] [0.109 [0.198] [0.102] Period 0.445*** 0.195*** 0.545*** 0.243*** [0.037] [0.022] [0.041] [0.021] Period Squared ‐0.015*** ‐0.008*** ‐0.018*** ‐0.011*** [0.001] [0.001] [0.001] [0.001] Risk ‐0.061 ‐0.089*** ‐0.126** ‐0.055* [0.054] [0.032] [0.059] [0.031] Raven Test 0.201*** 0.009 0.182*** 0.031* [0.032] [0.019] [0.035] [0.018] Sex 0.664*** 0.179* 0.743*** 0.223** [0.168] [0.101] [0.184] [0.099] Constant 5.784*** 3.203*** 5.072*** 4.171*** [1.267] [0.766] [1.391] [0.720] Observations 1361 1361 1361 1361 R‐squared 0.18 0.09 0.16 0.15 Standard errors in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

TABLE 4: BEHAVIORAL ANALYSIS SIGMA =0.50 SIGMA= 0.28 CONSUMPTION EXANTE EXPOST EXANTE EXPOSTOptimal consumption 0.101 0.888*** 0.228*** 0.524*** 0.006 0.453*** 0.131*** 0.348***

[0.129] [0.130] [0.079] [0.083] [0.063] [0.063] [0.046] [0.046]

Income 0.356*** 0.348*** 0.363*** 0.342***

[0.024] [0.023] [0.025] [0.023]

Available cash ‐0.009 0.002 ‐0.017* ‐0.001

[0.007] [0.007] [0.009] [0.007]

Observations 1361 1361 1361 1361 1361 1361 1361 1361

R‐squared 0.39 0.29 0.39 0.29 0.39 0.29 0.39 0.29

Standard errors in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

24

FIGURE 1: CONSUMPTION IN TREATMENT LS10

050

100

150

Ave

rage

Con

s.

0 5 10 15 20 25 30period

Actual Cons. Ex-ante Cons. sig=0.50Ex-post Cons. sig= 0.50

Average Consumption (R=10)

050

100

150

Ave

rage

Con

s.

0 5 10 15 20 25 30period



25

FIGURE 2: CUMULATIVE SAVINGS IN TREATMENT LS10

050

100

150

Av.

Cum

. Sav

ings

.

0 5 10 15 20 25 30period

Actual Cum. Savs. Ex-ante Cum. Savs. sig=0.50Ex-post Cum. Savs. sig= 0.50

Av. Cum. Savings (R=10)

050

100

150

Av.

Cum

. Sav

ings

.

0 5 10 15 20 25 30period



26

FIGURE 3: CONSUMPTION IN TREATMENT LS15

050

100

150

Ave

rage

Con

s.

0 5 10 15 20 25 30period



050

100

150

Ave

rage

Con

s.

0 5 10 15 20 25 30period



27

FIGURE 4: CUMULATIVE SAVINGS IN TREATMENT LS15

050

100

150

Av.

Cum

. Sav

ings

.

0 5 10 15 20 25 30period



050

1001

50Av.

Cum

. Sav

ings

.

0 5 10 15 20 25 30period



28

Footnotes

1 See Gruber and Wise (1997) or Blondal and Scarpetta (1998). 2 Many studies have analyzed the relationship between retirement and Social Security. Earlier literature mainly focussed on the effect of the introduction of a pension system on the individual retirement decision, see among others, Feldstein (1977), Sheshinski (1978), Kotlikoff (1979a; 1979b), Crawford and Lilien (1981) or Cremer and Pestieau (2000). There is however more recent literature dealing with the retirement decision in a political economy environment, see Crettez and Le Maitre (2002), Conde-Ruiz et al. (2003; 2005), Conde-Ruiz and Galasso (2003; 2004), Casamatta et al. (2005), or Lacomba and Lagos (2006; 2007). 3 The link between lifetime contributions and benefits is being reinforced in a number of countries, Germany, Italy, Hungary, Mexico, Poland, Sweden, etc., by shifting from defined-benefit to defined-contribution systems. See Blondal and Scarpetta (1998). 4 An alternative way of raising the effective retirement age might be to delay the legal retirement age. If so, Lacomba and Lagos (2007) find that it would be appropriate to combine that measure with an increase in the redistributive character of the pension system. This higher intra-generational redistribution would delay the preferred legal retirement age of most of voters, which would result in a larger degree of approval in the postponement of the legal retirement age. 5 In a theoretical background it also requires that F(T)=0. 6 For the sake of simplicity we choose a zero discount rate. 7 Conditions for risk aversion are u′(c)>0 and u′′(c)<0. The Inada conditions imply that u′(0)=∞ and u′(∞)=0. The specific utility function for implementing the experiment is u(c) = 10 * Square Root (c). 8 For the sake of simplicity we choose a zero discount rate. 9 Reforms aiming to achieve actuarially fair social security systems must adjust pension benefits to achieve that the increase in pension benefits be exactly offset by the higher cost in terms of contributions and foregone pensions. 10 The electronic recruitment system at LINEEX follows a quite natural mechanism. The University of Valencia students get an email from the laboratory, announcing new sessions. They then go to a web based system to register in a given session, depending on their prior experience and the session requirements. The risk aversion test was the one by Holt and Laury (2002), based on a menu of ten paired lottery choices. Decisions in our experiment were matched with the decisions in the test by a common random code subjects used in both sessions. Identities were never linked to choices. The basic design is explained in the appendix. 11 As the conversion involves no uncertainty at all, this parameter is only a design artifact to generate a concave payoff function and allow for some consumption smoothing. Similar design features have been used in the related literature, described in section 2. 12 We denote by earliest periods the pre lump-sum rounds, that is, the 10 first rounds in LS10 and the 15 first rounds in LS15. 13 Additional socioeconomic variables, as Edumother and Edufather (controlling for the education level of mother and father), are excluded from the analysis as they proved to be never significant in all estimations. Full estimations are available from authors upon request. 14 Fixed effects are included to adjust for the possibility that some subjects saved more than others. The estimates of those variables are omitted for the sake of simplicity. Although not in the table, we have also performed the analysis by sequence for any of the treatments. Since the results do not change we only present results by pooled data.

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